Diagram of Work done.
similarly resisted by the purely tensile force Ft. A force diagram
being drawn for each case,
Fc - fi Fs and Ft = ,/JTF,
Nature of Tensile and Compressive Stresses. — When
a plain tin-notched bar is broken by pulling, lines of cleavage
appear on the surface, inclined at 45° to the axis ; and the final
fracture is cup-shaped. Compression fractures are also inclined
at 45° and are often wedge-shaped. The evident deduction is
that rupture takes place on shear planes in both cases, and that
the three simple stresses are interdependent.
Work done by Uniform Forces. — The unit of work is
a foot-pound, or one pound exerted through a distance of one foot.
One pound acting through two feet, or two pounds through one
foot, are each two foot-pounds. Hence :
Work = pressure x distance
= pounds x feet = foot-pounds.
These forming a product may be represented by an area, for
length x breadth == area, and A, Fig. 325, is therefore the diagram
of work with uniform force :
Work done = pounds x feet ~ o x x o Y ~ area A.
Work done by Variable Forces is shewn by diagram atB,
Fig. 325, As the body moves from ox to 5, the pressure varies
as GJ xp 2 &, Sic. Now, work done between o'j and i can neither
be ox KX x i ft nor i a x i ft, but must be the average of these,
or O-L /x i. In like manner the other dotted rectangles shew the
work between the remaining intervals, and their addition,
Area ox xx b vx « work done.
Work done in Deformii^g a Bar is found at r, Fig. 326.
Divide o B into ten parts, and erect pei^endiculars between the
divisions. Measure the vertical ordinates in tons, then
Total of orflnates ^ ^ ^ .
me»n load x extension*^ work in inch tons. ($ee#. 1065.)